Earlier today Sherman tweeted that the Mariners have interest in Damon. Larry Stone of the Seattle Times looks more deeply at the Mariners-Damon connections over the years. He also provides this nugget, which he has never confirmed with Damon:

I heard from someone who works around the Mariners that after Bill Bavasi was fired in 2008, and the Mariners were searching for a new general manager, Damon actually was telling people he would be interested in the job. This person insisted that Damon seemed dead serious, even though he was still an active player.

We haven't heard much else about possible destinations for Damon. Perhaps the Mets or Cardinals would consider him, but I'm just speculating.